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JEE Main 2019 (12 Jan, Shift 1) · Magnetic Field of Straight Wires

Magnetic Field of Straight Wires question from JEE Main 2019 (12 Jan, Shift 1)

Q61JEE Main 2019 · 12 JAN · SHIFT 1Difficult

Magnetic Field of Straight Wires

As shown in the figure, two infinitely long, identical wires are bent by 90° and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y- axis. If OP = OQ = 4cm, and the magnitude of the magnetic field at O is 10–4 T, and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at O will be (μ\mu0 = 4π×\pi \times 10–7 NA–2):

Figure

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Answer: (c)

  1. LP and QM lie on the x-axis through O, so they give zero field.
  2. PS and QN are semi-infinite, each starting at the foot of the perpendicular from O at d=4d = 4 cm: μ0I4πd\frac{\mu_0 I}{4\pi d} each, both into the page.
  3. B=μ0I2πd=2×10−7I0.04=5×10−6IB = \frac{\mu_0 I}{2\pi d} = \frac{2 \times 10^{-7} I}{0.04} = 5 \times 10^{-6} I
  4. 5×10−6I=10−4⇒I=205 \times 10^{-6} I = 10^{-4} \Rightarrow I = 20 A
  5. So the answer is (c) 20 A, into the page.
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